A User's Guide to Measure Theoretic Probability
A User's Guide to Measure Theoretic Probability
This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.
- Numerous exercises
- Contains many comments, explanations and aids to intuition, not just wall-to-wall mathematics
- Unusual treatment of advanced topics, using streamlined notation and methods accessible to students who have not studied probability at this level before
Reviews & endorsements
"Unlike technical books of a previous generation, here we have an author admitting that a reader might find the subject difficult and even offering a window on the pedagogical considerations by which he shapes his exposition. Pollard does not just explain and clarify abstractions; he really sells them to a presumably skeptical reader. Thus he bridges a gap in the literature, between elementary probability texts and advanced works that presume a secure prior knowledge of measure theory...The nice layout and occasional useful diagram further amplify the friendliness of this book." Choice
"The book ... can be recommended as an excellent source in measuring theoretic probability theory as well as a handbook for everybody who studies stochastic processes in the real world." Mathematical Reviews
Product details
December 2001Paperback
9780521002899
366 pages
255 × 179 × 23 mm
0.652kg
200 exercises
Available
Table of Contents
- 1. Motivation
- 2. A modicum of measure theory
- 3. Densities and derivatives
- 4. Product spaces and independence
- 5. Conditioning
- 6. Martingale et al
- 7. Convergence in distribution
- 8. Fourier transforms
- 9. Brownian motion
- 10. Representations and couplings
- 11. Exponential tails and the law of the iterated logarithm
- 12. Multivariate normal distributions
- Appendix A. Measures and integrals
- Appendix B. Hilbert spaces
- Appendix C. Convexity
- Appendix D. Binomial and normal distributions
- Appendix E. Martingales in continuous time
- Appendix F. Generalized sequences.
